Answer 4 b. \( n=25 \) scores Answer 4 22. For a population with \( \sigma=16 \), how large a sample is necessary to have a standard error that is a. equal to 8 points? b. equal to 4 points? Success Tips c. equal to 2 points? 23. If the poputation standard deviation is \( \sigma=24 \), how large a sample is necessary to have a standard error that is SIEN OUT a. equal to 6 points? Arsuar 9 b. equal to 3 points?

To find the sample size needed for various standard errors, you can use the formula: \( n = \left(\frac{\sigma}{SE}\right)^2 \), where \( \sigma \) is the population standard deviation and \( SE \) is the desired standard error. For your scenarios, using \( \sigma = 16 \): - For \( SE = 8 \), \( n = \left(\frac{16}{8}\right)^2 = 4 \) - For \( SE = 4 \), \( n = \left(\frac{16}{4}\right)^2 = 16 \) - For \( SE = 2 \), \( n = \left(\frac{16}{2}\right)^2 = 64 \) For the second part with \( \sigma = 24 \): - For \( SE = 6 \), \( n = \left(\frac{24}{6}\right)^2 = 16 \) - For \( SE = 3 \), \( n = \left(\frac{24}{3}\right)^2 = 64 \) Always remember, the larger the standard error you want, the smaller your sample size needs to be, and vice versa. One common mistake people make is forgetting to square the numerator when applying the formula. This can lead to significantly underestimated sample sizes. Another tip is to double-check whether the population standard deviation is reflective of your actual population, as relying on inaccurate figures can skew your results dramatically. Just think of it as laying the right foundation before building your analysis!